Cut points in Čech-Stone remainders

Abstract

We investigate cut points of subcontinua of β R ∖ R \beta \mathbb {R}\backslash \mathbb {R} . We find, under CH, the topologically smallest type of subset of R \mathbb {R} that can support such a cut point. On the other hand we answer Question 66 of Hart and van Mill’s Open problems on β ω \beta \omega [Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North-Holland, Amsterdam, 1990, pp. 97-125] by showing that it is consistent that all cut points are trivial (in a sense to be made precise in the paper).